feat: show projected runestone gain persistently in resource bar

Adds computeProjectedRunestones() to the shared tick engine using the
correct server-side formula (cbrt, (count+1)^2 threshold). The resource
bar now shows a persistent '+N On Prestige' row so players can always
see what they would earn. The prestige panel's own preview was also
fixed to use the shared helper, replacing a broken local calculation
that used sqrt and the wrong threshold formula.

Closes #168

apps/web/src/components/game/prestigePanel.tsx

@@ -12,25 +12,27 @@ import { useState, type JSX } from "react";
 import { prestige } from "../../api/client.js";
 import { useGame } from "../../context/gameContext.js";
 import {
-  PRESTIGE_UPGRADES,
   PRESTIGE_UPGRADE_CATEGORY_LABELS,
+  PRESTIGE_UPGRADES,
 } from "../../data/prestigeUpgrades.js";
+import {
+  computeProjectedRunestones,
+} from "../../engine/tick.js";
 import { cdnImage } from "../../utils/cdn.js";
 import { sendNotification } from "../../utils/notification.js";
 import { playSound } from "../../utils/sound.js";
 import type { PrestigeUpgradeCategory } from "@elysium/types";
 
 const baseThreshold = 1_000_000;
-const thresholdScale = 5;
-const runestonesPerLevel = 10;
 
 /**
  * Calculates the prestige threshold for a given prestige count.
+ * Mirrors the server formula: BASE * (count + 1)^2.
  * @param prestigeCount - The current prestige count.
  * @returns The required gold to prestige.
  */
 const calculateThreshold = (prestigeCount: number): number => {
-  return baseThreshold * Math.pow(thresholdScale, prestigeCount);
+  return baseThreshold * Math.pow(prestigeCount + 1, 2);
 };
 
 /**
@@ -42,32 +44,6 @@ const calculateProductionMultiplier = (prestigeCount: number): number => {
   return Math.pow(1.15, prestigeCount);
 };
 
-/**
- * Calculates the runestone preview for a prestige.
- * @param totalGoldEarned - Total gold earned this run.
- * @param prestigeCount - The current prestige count.
- * @param purchasedUpgradeIds - IDs of purchased prestige upgrades.
- * @returns The predicted runestone reward.
- */
-const calculateRunestonePreview = (
-  totalGoldEarned: number,
-  prestigeCount: number,
-  purchasedUpgradeIds: Array<string>,
-): number => {
-  const threshold = calculateThreshold(prestigeCount);
-  const base
-    = Math.floor(Math.sqrt(totalGoldEarned / threshold)) * runestonesPerLevel;
-  const runestoneMult = PRESTIGE_UPGRADES.filter((upgrade) => {
-    return (
-      upgrade.category === "runestones"
-      && purchasedUpgradeIds.includes(upgrade.id)
-    );
-  }).reduce((mult, upgrade) => {
-    return mult * upgrade.multiplier;
-  }, 1);
-  return Math.floor(base * runestoneMult);
-};
-
 const categoryOrder: Array<PrestigeUpgradeCategory> = [
   "income",
   "click",
@@ -114,11 +90,7 @@ const PrestigePanel = (): JSX.Element => {
   const { autoAdventurer, prestige: prestigeData, player } = state;
   const threshold = calculateThreshold(prestigeData.count);
   const isEligible = player.totalGoldEarned >= threshold;
-  const runestonePreview = calculateRunestonePreview(
-    player.totalGoldEarned,
-    prestigeData.count,
-    prestigeData.purchasedUpgradeIds,
-  );
+  const runestonePreview = computeProjectedRunestones(state);
   const nextMultiplier = calculateProductionMultiplier(prestigeData.count + 1);
 
   async function handlePrestige(): Promise<void> {

apps/web/src/components/ui/resourceBar.tsx

@@ -15,6 +15,7 @@ import {
   computeEssencePerSecond,
   computeGoldPerSecond,
   computePartyCombatPower,
+  computeProjectedRunestones,
 } from "../../engine/tick.js";
 import type { Resource } from "@elysium/types";
 
@@ -89,10 +90,12 @@ const ResourceBar = ({
   let partyCombatPower = 0;
   let goldPerSecond = 0;
   let essencePerSecond = 0;
+  let projectedRunestones = 0;
   if (state !== null) {
     partyCombatPower = computePartyCombatPower(state);
     goldPerSecond = computeGoldPerSecond(state);
     essencePerSecond = computeEssencePerSecond(state);
+    projectedRunestones = computeProjectedRunestones(state);
   }
 
   let avatarUrl: string | null = null;
@@ -234,6 +237,13 @@ const ResourceBar = ({
                 </span>
                 <span className="resource-label">{"Runestones"}</span>
               </div>
+              <div className="resource">
+                <span className="resource-icon">{"⭐"}</span>
+                <span className="resource-value">
+                  {`+${formatNumber(projectedRunestones)}`}
+                </span>
+                <span className="resource-label">{"On Prestige"}</span>
+              </div>
               <div className="resource">
                 <span className="resource-icon">{"⚔️"}</span>
                 <span className="resource-value">

apps/web/src/engine/tick.ts

@@ -447,6 +447,36 @@ export const computePartyCombatPower = (state: GameState): number => {
     * companionCombatMult;
 };
 
+const basePrestigeThreshold = 1_000_000;
+const runestonesPerPrestigeLevelClient = 15;
+const maxBaseRunestones = 200;
+
+/**
+ * Computes the projected runestone reward if the player were to prestige right now.
+ * Mirrors the server-side calculateRunestones formula exactly.
+ * @param state - The current game state.
+ * @returns The number of runestones the player would earn from a prestige now.
+ */
+export const computeProjectedRunestones = (state: GameState): number => {
+  const { count, purchasedUpgradeIds } = state.prestige;
+  const threshold = basePrestigeThreshold * Math.pow(count + 1, 2);
+  const base = Math.min(
+    Math.floor(Math.cbrt(state.player.totalGoldEarned / threshold))
+    * runestonesPerPrestigeLevelClient,
+    maxBaseRunestones,
+  );
+  const gain1Mult = purchasedUpgradeIds.includes("runestone_gain_1")
+    ? 1.25
+    : 1;
+  const gain2Mult = purchasedUpgradeIds.includes("runestone_gain_2")
+    ? 1.5
+    : 1;
+  const runestoneMult = gain1Mult * gain2Mult;
+  /* eslint-disable-next-line @typescript-eslint/no-unsafe-assignment -- optional chained game state field */
+  const echoMult: number = state.transcendence?.echoRunestoneMultiplier ?? 1;
+  return Math.floor(base * runestoneMult * echoMult);
+};
+
 /**
  * Pure function — applies one game tick to the state.
  * DeltaSeconds: time elapsed since last tick.